while true loop

Generally, yes - when you call execute(), the Robocode engine processes one tick, including firing all the events on your bot, and then your run() method continues executing. So most of us have an infinite loop that calls execute() at the end, and each iteration is one tick.

But there's no magic to it - you could have a run method that goes:

public void run() {
  turnRight(20);
  ahead(100);
  fire(3);
}

And that would be perfectly valid. Or you could call execute() every third iteration of your loop. In Dookious, my run method used to have a loop that was while (notWonYet) ..., then a victory dance.